.\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
.\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk
.\"     <mtk.manpages@gmail.com>
.\"
.\" SPDX-License-Identifier: GPL-1.0-or-later
.\"
.\" based on glibc infopages
.\"
.TH lgamma 3 2023-02-05 "Linux man-pages 6.03"
.SH NAME
lgamma, lgammaf, lgammal, lgamma_r, lgammaf_r, lgammal_r, signgam \-
log gamma function
.SH LIBRARY
Math library
.RI ( libm ", " \-lm )
.SH SYNOPSIS
.nf
.B #include <math.h>
.PP
.BI "double lgamma(double " x );
.BI "float lgammaf(float " x );
.BI "long double lgammal(long double " x );
.PP
.BI "double lgamma_r(double " x ", int *" signp );
.BI "float lgammaf_r(float " x ", int *" signp );
.BI "long double lgammal_r(long double " x ", int *" signp );
.PP
.BI "extern int " signgam ;
.fi
.PP
.RS -4
Feature Test Macro Requirements for glibc (see
.BR feature_test_macros (7)):
.RE
.PP
.nf
.BR lgamma ():
    _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L || _XOPEN_SOURCE
        || /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
.fi
.PP
.BR lgammaf (),
.BR lgammal ():
.nf
    _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
        || /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
.fi
.PP
.BR lgamma_r (),
.BR lgammaf_r (),
.BR lgammal_r ():
.nf
    /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
.fi
.PP
.IR signgam :
.nf
    _XOPEN_SOURCE
        || /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
.fi
.SH DESCRIPTION
For the definition of the Gamma function, see
.BR tgamma (3).
.PP
The
.BR lgamma (),
.BR lgammaf (),
and
.BR lgammal ()
functions return the natural logarithm of
the absolute value of the Gamma function.
The sign of the Gamma function is returned in the
external integer
.I signgam
declared in
.IR <math.h> .
It is 1 when the Gamma function is positive or zero, \-1
when it is negative.
.PP
Since using a constant location
.I signgam
is not thread-safe, the functions
.BR lgamma_r (),
.BR lgammaf_r (),
and
.BR lgammal_r ()
have been introduced; they return the sign via the argument
.IR signp .
.SH RETURN VALUE
On success, these functions return the natural logarithm of Gamma(x).
.PP
If
.I x
is a NaN, a NaN is returned.
.PP
If
.I x
is 1 or 2, +0 is returned.
.PP
If
.I x
is positive infinity or negative infinity,
positive infinity is returned.
.PP
If
.I x
is a nonpositive integer,
a pole error occurs,
and the functions return
.RB + HUGE_VAL ,
.RB + HUGE_VALF ,
or
.RB + HUGE_VALL ,
respectively.
.PP
If the result overflows,
a range error occurs,
.\" e.g., lgamma(DBL_MAX)
and the functions return
.BR HUGE_VAL ,
.BR HUGE_VALF ,
or
.BR HUGE_VALL ,
respectively, with the correct mathematical sign.
.SH ERRORS
See
.BR math_error (7)
for information on how to determine whether an error has occurred
when calling these functions.
.PP
The following errors can occur:
.TP
Pole error: \fIx\fP is a nonpositive integer
.I errno
is set to
.B ERANGE
(but see BUGS).
A divide-by-zero floating-point exception
.RB ( FE_DIVBYZERO )
is raised.
.TP
Range error: result overflow
.I errno
is set to
.BR ERANGE .
An overflow floating-point exception
.RB ( FE_OVERFLOW )
is raised.
.\" glibc (as at 2.8) also supports an inexact
.\" exception for various cases.
.SH STANDARDS
The
.BR lgamma ()
functions are specified in C99, POSIX.1-2001, and POSIX.1-2008.
.I signgam
is specified in POSIX.1-2001 and POSIX.1-2008, but not in C99.
The
.BR lgamma_r ()
functions are nonstandard, but present on several other systems.
.SH BUGS
In glibc 2.9 and earlier,
.\" http://sources.redhat.com/bugzilla/show_bug.cgi?id=6777
when a pole error occurs,
.I errno
is set to
.BR EDOM ;
instead of the POSIX-mandated
.BR ERANGE .
Since glibc 2.10, glibc does the right thing.
.SH SEE ALSO
.BR tgamma (3)
